$A$ $B$ $C$ If: $ AC = 143$, $ BC = 8x + 4$, and $ AB = 7x + 4$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {7x + 4} + {8x + 4} = {143}$ Combine like terms: $ 15x + 8 = {143}$ Subtract $8$ from both sides: $ 15x = 135$ Divide both sides by $15$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $BC$ $ BC = 8({9}) + 4$ Simplify: $ {BC = 72 + 4}$ Simplify to find ${BC}$ : $ {BC = 76}$